TY  - THES
AB  - In analogy to the theory of classical Jacobi forms which has proven to
have various important applications ranging from number theory to
physics, we develop in this thesis a theory of Jacobi forms over
arbitrary totally real number fields.  For this end we need to
develop, first of all, a theory of finite quadratic modules over
number fields and their associated Weil representations.  As a main
application of our theory, we are able to describe explicitly all
singular Jacobi forms over arbitrary totally real number fields whose
indices have rank 1. We expect that these singular Jacobi forms play
a similar important role in this new founded theory of Jacobi forms
over number fields as the Weierstrass sigma function does in the
classical theory of Jacobi forms.
AU  - Boylan, Hatice
DA  - 2011
KW  - Jacobi-Form
KW  - singuläre Jacobiformen
KW  - Jacobiformen über Zahlkörpern
KW  - Theta Reihen
KW  - Weil Darstellungen
KW  - Jacobi forms over number fields
KW  - theta series
KW  - Weil representations
LA  - eng
PY  - 2011
TI  - Jacobi forms, finite quadratic modules and Weil representations over number fields
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:467-5970
Y2  - 2024-12-26T21:11:17
ER  -